Problem: Multiply the following complex numbers: $({-1}) \cdot ({3+3i})$
Explanation: Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({-1}) \cdot ({3+3i}) = $ $ ({-1} \cdot {3}) + ({-1} \cdot {3}i) + ({0}i \cdot {3}) + ({0}i \cdot {3}i) $ Then simplify the terms: $ (-3) + (-3i) + (0i) + (0 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ -3 + (-3 + 0)i + 0i^2 $ After we plug in $i^2 = -1$ , the result becomes $ -3 + (-3 + 0)i - 0 $ The result is simplified: $ (-3 - 0) + (-3i) = -3-3i $